Simulation of Effects of Learned Trap Response on Three Estimators of Population Size

Abstract

Evaluation of the Schnabel, geometric and nonparametric estimators of population size was performed on a model population of 100 individuals which possessed a bivariate normal home range model with ox = 1 and a, = 2, a random spatial pattern, an average initial probability of capture of p = 0.10 or p = 0.40 and either a trap happy or trap shy learning process. Data were generated from a model which simulated 10-sample mark-recapture experiments consisting of 25 traps. Evaluation of these estimators reveals the magnitude of bias and variability present in such circumstances. The results indicate that the nonparametric estimator was the most robust under these conditions. J. WILDL. MANAGE. 43(2):474-483 Estimating the size of an animal population presents complex problems to population ecologists. General reviews of some of the methods were presented by Overton (1969) and Seber (1973). Estimators which have been developed are based on various assumptions, some of which are not fully satisfied in practice. When assumptions are not satisfied, wide variation may result in the estimates. Since many different estimators are available, it is desirable to evaluate their performance under varying degrees of violation of the assumptions. This would provide the investigator a measure of the degree of robustness of the estimators and shed light into which one would be most suitable for a specific problem. Field evaluation of the estimators is possible if mark-recapture experiments are performed in areas where the true sizes of the populations are known. However, this information is rarely available. An alternate approach for determining the robustness of the estimators is to develop simulation models to mimic populations exposed to mark-recapture experiments. In such models the parameters that control the animals' response to trapping can be varied, resulting in differential magnitudes of assumption violation. Recently, simulation has been used in the study of estimators of population parameters. Gates (1969) used computer simulation to evaluate the bias of a variety of line transect density estimators. Burnham and Overton (1969) and Manly (1970) employed computer simulation in evaluating the behavior of various markrecapture estimators. In another paper, Manly (1971) used simulation to examine Jolly's (1965) variance formulas for estimators of population parameters. In the present study, computer simulation techniques were also used. The objective of this work was to evaluate the sample expectation, variance, bias, and mean square error of mark-recapture estimators of population size when the assumption of equal probability of capture of animals is violated in response to a learning process related to the previous capture history. Appreciation is extended to the Division of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, and to the Department of Fisheries and Wildlife, Michigan State University, East Lan' Present address: Department of Fisheries and Wildlife, Michigan State University, East Lansing, MI 48824. 474 J. Wildl. Manage. 43(2):1979 This content downloaded from 157.55.39.80 on Fri, 22 Apr 2016 05:57:59 UTC All use subject to http://about.jstor.org/terms SIMULATION OF LEARNED TRAP RESPONSE *Zarnoch 475 sing, Michigan, for computer time used in the development of the model and evaluation of the estimators of population size. ESTIMATORS OF POPULATION SIZE Letting N = number of individuals in the population and S = number of samples taken, the following estimators were evaluated. Schnabel.-The Schnabel estimator, modified by Chapman (1952), is defined